Well, I have some progress. I picked up the Dark Mountain Arms Stowaway in 5.7. It's a really neat design, but the trigger is an adventure. So I've been hacking on my mechanicals, of course, and I have it to where it's serviceable - kind of a redneck 2-stage feel.
Anyway, mine will chamber 60 TMKs out to 1.760", though that's leaving the boat tail inside the neck - I used 1.720". So with a tiny charge of Lil-Gun (under 10 grains), I'm getting 2300+ fps out of that bullet and 16" barrel. That gives me (my kids I mean) a 200-yd expansion window and point blank range. Out of a 3-lb gun.
For us 200-yd deer hunters, when a 223 is too much (I don't need an elk gun!), this might be just right (for our kids, that is). I should be doing some terminal testing in just over a month.